# 20. Calibration – Measurement Uncertainty Definitions and Sources

2020-11-24

For measurement uncertainties, the following uncertainties are explained below:

**Measurement Uncertainty**– Parameters with measurement result relevance to represent measurand’s distribution level.

**Standard Uncertainty**[**u(x****i****)**] – Use standard differences to represent the measurand’s uncertainty.

**Combined Standard Uncertainty**[**u****c****(y)**] – Combination of all standard uncertainty when measurement results were obtained from multiple sources.

**Expanded Uncertainty**(**U**) – The expected distribution range for the measurand with high probability, this is under a defined measurement result interval.

And in general, measurement standard uncertainty can be broken down into two different types:

**Type A standard uncertainty**: Use standard statistical analysis for single or multiple sets of measurement and respective error (used to be called random error).

**Type B standard uncertainty**: Evaluate systematic error and refer to the variance quantity (if it exists) to evaluate variance, standard deviation, average and degrees of freedom (DoF) for measurement uncertainty variance.

For other terminology used, here are the following list:

**Quantity (measurable quantity) –**can quantize determined phenomenon, object or material characteristics- Normal quantity: length, time, resistance…etc.
- Specified quantity: length of rod, wire resistance…etc.

**Value (of a quantity) –**Use numbers and appropriate measurement unit to represent quantity.

**True Value (of a quantity) –**Perfect and idea value from actual situations.

**Conventional true value (of a quantity) –**value to replace true value. Usually applied to capability comparison on calibration (national lab comparison scale).

**Measurement –**Operation to determine measured value (measurand).

**Measurand (Y) –**Measured value

**Influence Quantity –**A value which influence the measurand without measurement.

**Result of a Measurement –**value obtained from measurement.

**Uncorrected Result –**Measurement result before systematic error adjustment.

**Corrected Result –**Adjusted measurement result after considering systematic error.

**Accuracy of measurement –**Proximity between measurement result and true value (conventional true value)

**Measurement Error –**Differences when measurand subtract true value.

**Random Error –**Use numbers and appropriate measurement unit to represent quantity.

**Systematic Error –**Differences when multiple measurement’s average subtract the true value when measurement is repeatable.

**Correction –**Use adjustment for the non-adjusted measurement result to compensate system error. (same as systematic error, but opposite signs)

**Probability –**Chances occur for event randomly from 0 to 1.

**Confidence Interval –**The range for value to fall in under finite probability or confidence level.

**Confidence Level (p) –**A level of confidence to expect when the value falls into the region. Generally use 95% for uncertainty evaluation.

**Coverage Factor (k) –**A factor used for combining standard uncertainty to obtain extended uncertainty.

- Repeatability of Measurement Result indicates the proximity for the same measurand’s measurement result comparison under SAME CONDITION. It can indicate quantitative representation of measurand’s distribution within the same condition.

- Reproducibility of Measurement Result indicates the proximity for the same measurand’s measurement result comparison under DIFFERENT CONDITION. It can indicate quantitative representation of measurand’s distribution within different condition.

Lastly, the condition factors are listed as the following, but not limited to:

- Measurement Method
- Observer (Appraiser)
- Measuring Equipment/Instrument
- Location
- Usage Condition / Parameter Setup
- Time Period